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Juct check it for me

  1. Apr 10, 2004 #1
    Hiiiiiiiiiii everyone
    I've these two waves
    I need to find the resultant wave (y1+y2)
    I got that answer:

    y= 7 cos(wt+45) sin(kx+45)
    is that right?? plz if not give me a hint

    ==================My efforts=============================
    I added the amplidtude mathematically
    then using trigonometric rules i added the two "sin" and "cos" functions
    but i still need to know if my answer is true

  2. jcsd
  3. Apr 10, 2004 #2


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    The addition formula that I have for the sum of waves with different amplitudes is:

    [tex] A cos(x) + B sin(x) = \sqrt {A^2 + B^2} cos(x \pm \delta) [/tex]
    [tex] tan( \delta) = \frac {sin \delta} {cos \delta} = \pm \frac B A [/tex]
  4. Apr 10, 2004 #3
    What is that segma?
  5. Apr 10, 2004 #4
    and what about if...

    What about if "x" is not equal in both equations??
  6. Apr 10, 2004 #5

    The arguments for the sin and cos in your identity are both x. I may be missing a simplification you're seeing, but he's got one wave going left and one going right, so his arguments aren't the same.

    I tried using the identities for the sum and difference of two angles, but nothing cancelled, so it just got messy. But like I said, I may be missing something.
  7. Apr 10, 2004 #6


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    yeah it gets a little messy but:

    [tex] 3 \sin {(kx-\omega t)}= 3( \sin{kx} \cos{\omega t }- \sin{\omega t} \cos {kx} )[/tex]
    [tex] 4\cos{(kx+\omega t)}= 4(\cos{kx} \cos {\omega t}+ \sin{kx} \sin{\omega t})[/tex]
    add these together to get

    [tex]\cos {kx} (4 \cos {\omega t} - 3 \sin {\omega t})+ \sin{kx}(3 \cos {\omega t}+ 4 \sin{\omega t})[/tex]

    now apply the formula in my first post to the terms in parentheses.

    the [tex] \delta [/tex] (thats a low case delta) is defined in the second line of my first post.
    Last edited: Apr 10, 2004
  8. Apr 10, 2004 #7
    Integral, nicely done!

    Ok moham87, it doesn't look like your answer's right. But you've got your hint, so have at it! And watch those signs, or they'll kill you.
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